Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21433124 | C2 | semidirect |
| 3. #21422809 | C2 | semidirect |
| 4. #21422809 | C2 | semidirect |
| 5. #21422436 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1285 | C2 | semidirect |
| 56. C4⋊(C59⋊C8) | D4 | semidirect |
| 67. C4⋊C8×C59 | D4 | semidirect |
| 220. #1285 | D59 | semidirect |
| 250. C59 | #9457 | semidirect |
| 283. C4⋊C8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433124 | 2 |
| #21429038 | 2 |
| #21422809 | 2 |
| #21422436 | 2 |
| #21421952 | 2 |
| C59×#1285 | 2 |
| #9457 | 59 |